The payment of up to €1,000 is due to health employees who worked between March 1, 2020, and June 3, 2021.
The value to each eligible employee is based on their contracted hours in that time.
A spokesman for the HSE said determination as to who is eligible for the payment is made locally.
Around 100,000 are due the bonus payment in this round.
Health Minister Stephen Donnelly promised it would be paid “as soon as possible” in April.
Sinn Féin leader Mary Lou McDonald described the delay as “farcical” and said she had written to Taoiseach Micheál Martin about it.
Siptu health divisional organiser Kevin Figgis said he had sought updated figures on the number of staff who have received the bonus since June 3 but has not received them.
“The HSE has still issued nothing for health workers in the private sector,” he said.
“We have been consistently writing to the Department of Health in relation to our members on the private side, be they agency workers or contractors, or even other public servants not covered by the HSE or Section 38 agencies, who were part of the healthcare workforce like Dublin Fire Brigade.
“It’s simply unacceptable that those people continue to remain in the dark about how the department will recognise their efforts during the pandemic.”
In a letter to the HSE this month, the group of unions in the health sector – or staff panel, as it is known – said it was given a commitment that unions would receive a weekly update on sites where the bonus has been paid.
“This has not materialised,” says the letter from the staff panel’s chair, Tony Fitzpatrick.
“It is entirely unacceptable that the HSE appears to be unwilling or unable to engage with the trade unions in a timely manner; and the lack of progress in relation to the payment of the pandemic bonus is unacceptable, given the commitment by Mr Donnelly.”
Ms McDonald said that “18 months after it was first discussed by Government and six months after it was agreed, the fact that tens of thousands of healthcare workers are still waiting to receive a pandemic recognition payment is frankly farcical at this stage”.
“The delay is a failure of leadership, and it is downright disrespectful to our frontline healthcare heroes and their sacrifices,” she said.
“This payment was the least that the Government could do, but even this simple payment has become a disaster of mismanagement.
“It should have been an opportunity to show them that the political system recognises and values the contribution of those on the front line. Instead they have been met with foot-dragging and excuses.
“Each and every one of these workers made enormous personal sacrifices and risked their health and their lives to keep us safe. They truly went above and beyond the call of duty.
“I have written to the Taoiseach to express my serious concern and I have called on him to intervene directly to ensure that the payment of the bonus to our frontline workers happens without further delay.”